Mr. Integral
Math notes/Pre-Calculus/Trigonometry

Ratios in a Right Triangle — Cheat sheet

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The three ratios

FunctionRatio
sin⁡θ\sin\thetaopposite / hypotenuse
cos⁡θ\cos\thetaadjacent / hypotenuse
tan⁡θ\tan\thetaopposite / adjacent

The other three

FunctionRatioAlso equals
cot⁡θ\cot\thetaadjacent / opposite1/tan⁡θ1/\tan\theta
sec⁡θ\sec\thetahypotenuse / adjacent1/cos⁡θ1/\cos\theta
csc⁡θ\csc\thetahypotenuse / opposite1/sin⁡θ1/\sin\theta

Checks

PointNote
Size does not mattersimilar triangles share every ratio
Boundsin⁡θ\sin\theta and cos⁡θ\cos\theta never exceed 11
Complementssin⁡θ=cos⁡(90∘−θ)\sin\theta = \cos(90^\circ - \theta)
"Opposite" movesthe names are relative to the angle, not the page
The other anglemove to it and the two legs trade names